Finite Group Databasebeta

← #16848022

Subgroups — #16848022

Order 3968.

112 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14521478C211yesmaximal, characteristic, complemented
2D16×D31C211yesmaximal, characteristic, complemented
3#14520888C211yesmaximal, characteristic, complemented
4#14520887C211yesmaximal, characteristic, complemented
5#14520884C211yesmaximal, characteristic, complemented
6#14520882C211yesmaximal, characteristic, complemented
7C31×D32C211yesmaximal, characteristic, complemented
8#11758489—21no—
9D8×D31—21no—
10C31×D16C2211yescharacteristic
11C31×D16C2211yescharacteristic, complemented
12#11758415—21no—
13#11758414—21no—
14Dic248C2211yescharacteristic, complemented
15D496C2211yescharacteristic
16C16×D31C2211yescharacteristic
17C31×C32C2211yescharacteristic, complemented
18C31⋊C32C2211yescharacteristic, complemented
19#92497—41no—
20D4×D31—41no—
21D8×C31—21no—
22D8×C31—21no—
23#92480—41no—
24#92479—41no—
25Dic124—21no—
26D248—21no—
27C8×D31D411yescharacteristic
28C16×C31C2311yescharacteristic
29C31⋊C16D411yescharacteristic
30C22×D31—81no—
31D4×C31—41no—
32D4×C31—41no—
33C22⋊D31—81no—
34C22⋊D31—81no—
35C2×Dic31—81no—
36D124—41no—
37C4×D31D811yescharacteristic
38Dic62—41no—
39C8×C31C2×D411yescharacteristic
40C31⋊C8D811yescharacteristic
41#2263—311nomaximal, Sylow
42C22×C31—81no—
43C22×C31—81no—
44C2×D31—81no—
45C2×D31—162no—
46C2×D31D1611yescharacteristic
47C4×C31C2×D811yescharacteristic
48Dic31—81no—
49Dic31D1611yescharacteristic
50#508—311no—
51C2×D16—311no—
52SD64—311no—
53SD64—311no—
54D32—311no—
55D32D3111yescharacteristic, complemented
56M64—311no—
57C2×C31—161no—
58C2×C31—161no—
59C2×C31C2×D1611yescharacteristic
60D31—21no—
61D31—161no—
62#135—621no—
63C2×D8—621no—
64Q32—311no—
65SD32—621no—
66D16—311no—
67D16—621no—
68D16C2×D3111yescharacteristic
69D16C2×D3111yescharacteristic, complemented
70C2×C16—311no—
71C32—311no—
72C32C2×D3111yescharacteristic, complemented
73C31#226311yescharacteristic, complemented, Sylow
74#41—1241no—
75C2×D4—1241no—
76Q16—621no—
77SD16—1241no—
78D8—21no—
79D8—21no—
80D8—621no—
81D8—1241no—
82C2×C8—311no—
83C16—311no—
84C16C22×D3111yescharacteristic
85C23—2481no—
86Q8—1241no—
87D4—41no—
88D4—41no—
89D4—1241no—
90D4—2481no—
91D4—2481no—
92C2×C4—311no—
93C2×C4—2481no—
94C8—311no—
95C8D4×D3111yescharacteristic
96C22—81no—
97C22—81no—
98C22—311no—
99C22—4962no—
100C22—2481no—
101C4—311no—
102C4—2481no—
103C4D8×D3111yescharacteristic
104C2—161no—
105C2—161no—
106C2—621no—
107C2—4961no—
108C2D16×D3111yescharacteristic
subgroupG/H
centerC2D16×D31
commutator, cosocleC16×C31C23
FrattiniC16C22×D31
FittingC31×D32C2
socleC2×C31C2×D16
hypercenterD32D31
hypocenterC31#2263
LCSG ▷ C16×C31 ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14521478C2semidirect
2. D16×D31C2semidirect
3. #14520888C2semidirect
4. #14520887C2semidirect
5. #14520884C2semidirect
6. #14520882C2semidirect
7. C31×D32C2semidirect
11. C31×D16C22semidirect
14. Dic248C22semidirect
17. C31×C32C22semidirect
18. C31⋊C32C22semidirect
55. D32D31semidirect
69. D16C2×D31semidirect
72. C32C2×D31semidirect
73. C31#2263semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145214782
D16×D312
#145208882
#145208872
#145208842
#145208822
C31×D322
#226331